For example, the complex electromagnetic permittivity \(\varepsilon (\omega )\)  of
dielectrics can be written as \(\varepsilon (\omega )=f(\omega ^{2})\) , where \(f\in \mathfrak {S}\) 
and \(\mathfrak {Im}(\omega )>0\)  [1]}, [2]}. Both the complex impedance and
admittance functions \(Z(\omega )\)  and \(Y(\omega )\) , respectively, of electric circuits
made of resistors, capacitors and inductive coils can be written as
\(Z(\omega )=i\omega f(\omega ^{2})\) , where \(f\in \mathfrak {S}\)  and \(\mathfrak {Im}(\omega )<0\) 
[3]}. In high energy physics it is the energy (or momentum) that
plays the role of the complex variable and the scattering amplitude is the Stieltjes function
[4]}, [5]}, [6]}, [7]}, [8]}. In the theory of binary conducting composites the
dependence of the effective conductivity \(\sigma ^{*}\)  of the composite on the
ratio \(h=\sigma _{2}/\sigma _{1}\)  of the conductivities of two constituents is also
expressible in terms of Stieltjes functions, [9]}, [10]}, [11]}, [12]}
\(\frac{\sigma ^{*}}{\sigma _{1}}=1+\left(1-\displaystyle \frac{1}{h}\right)f\left(-\displaystyle \frac{1}{h}\right),\qquad f\in \mathfrak {S}.\) 
